Chapter 2: FAQs 75
You would then only be exposed to basis risk. Be careful
with this because there may be times when the close
relationship breaks down.
If you have many financial instruments that are uncorre-
lated with each other then you can construct a portfolio
with much less risk than any one of the instruments
individually. With a large such portfolio you can theo-
retically reduce risk to negligible levels. Although this
isn’t strictly hedging it achieves the same goal.
Gamma hedging To reduce the size of each rehedge
and/or to increase the time between rehedges, and thus
reduce costs, the technique of gamma hedging is often
employed. A portfolio that is delta hedged is insensitive
to movements in the underlying as long as those move-
ments are quite small. There is a small error in this due
to the convexity of the portfolio with respect to the
underlying. Gamma hedging is a more accurate form of
hedging that theoretically eliminates these second-order
effects. Typically, one hedges one, exotic, say, contract
with a vanilla contract and the underlying. The quan-
tities of the vanilla and the underlying are chosen so
as to make both the portfolio delta and the portfolio
gamma instantaneously zero.
Vega hedging The prices and hedging strategies are only
as good as the model for the underlying. The key param-
eter that determines the value of a contract is the
volatility of the underlying asset. Unfortunately, this is a
very difficult parameter to measure. Nor is it usually a
constant as assumed in the simple theories. Obviously,
the value of a contract depends on this parameter,
and so to ensure that a portfolio value is insensitive to
this parameter we can vega hedge. This means that we
hedge one option with both the underlying and another
option in such a way that both the delta and the vega,
the sensitivity of the portfolio value to volatility, are